## Creativity in the context of Fermi problems

• In this paper, the formula for measuring creativity in Fermi problems is developed. Fermi problems are open problems, treated as a type of mathematical modelling, that requires a quick estimation of an unclear quantity. The problem usually requires decomposing and transforming the initial Fermi problem into understandable subproblems. It has been suggested that such decompositions and transformations require creativity. However, there are limited studies that analyze and discuss how creativity in Fermi problems should be viewed, although Fermi problems have potential related to creativity. Therefore, the author conducted empirical studies of Fermi problems from the perspective of creativity, based on previous studies on creativity. In previous studies, creativity is often measured by three factors: Fluency, Flexibility, and Originality. Fluency is measured by the number of ideas for solving a problem. Flexibility is measured by the number of categories of ideas for solving a problem. Originality is measured by the rarity of ideas to solve the problem. However, there are several criticisms of these measures. The first are criticisms of Flexibility. Because of the similarity between Fluency and Flexibility, some studies do not include Flexibility as a factor of creativity. Furthermore, the categorization of ideas is arbitrary, so the measurement of Flexibility could change depending on the evaluator. The second is a criticism of Originality. Most studies arbitrarily set the rarity of ideas to measure this factor. For example, some studies say that less than 5% of ideas are rare, while others say that less than 1% are rare. The formula to measure creativity in Fermi problems, which could resolve the above criticisms, is proposed. The formula is developed by applying information theory. It does not include the concept of Flexibility, which is evaluated in terms of the number of categories of ideas. Furthermore, the formula does not set a criterion for determining idea rarity, using as it does the relative occurrence rate of ideas. The results of the analysis using structural equation modeling, which is a statistical analysis, showed a more than moderate correlation between creativity calculated using the suggested formula and established creativity (e.g., creativity in psychology). Furthermore, the proposed formula performed better than a formula measuring creativity in a previous study. In other words, the proposed formula could solve the issues that have been pointed out in previous studies, and the statistical analysis allowed us to examine the formula.

Author: Hidemichi Okamoto urn:nbn:de:bsz:751-opus4-3632 Development and evaluation of a measurement instrument based on the analysis of creative aspects in solving Fermi problems Mutfried HartmannGND, Tetsushi Kawasaki, Frank ThissenGND Doctoral Thesis English 2022 2023/02/21 Pädagogische Hochschule Karlsruhe, Fakultät B - Fakultät für Natur- und Sozialwissenschaften (seit WS 19/20) 2023/02/16 2023/02/21 Evaluation; Fermi Aufgaben; Fermi-Probleme; Kreativität; MessinstrumentFermi problems; creativity; evaluation; measurement instrument Mathematikunterricht; Problemorientierter Unterricht; Lernaufgabe; Fermi, Enrico; Kreativität 183716617X Fakultät B - Fakultät für Natur- und Sozialwissenschaften (seit WS 19/20) / Institut für Mathematik und Informatik Veröffentlichungsvertrag für Dissertationen